1 citations · 1 across the 6 of their papers we have counts for
6 papers
Split-Merge: A Difference-based Approach for Dominant Eigenvalue Problem
Xiaozhi Liu, Mengmeng Song, Yong Xia
The computation of the dominant eigenpair for symmetric positive semidefinite matrices is fundamental in numerical optimization. This work shifts the paradigm from the classical Ra…
Linear programming on the Stiefel manifold
Mengmeng Song, Yong Xia
Linear programming on the Stiefel manifold (LPS) is studied for the first time. It aims at minimizing a linear objective function over the set of all -tuples of orthonormal vect…
On globally solving nonconvex trust region subproblem via projected gradient method
Mengmeng Song, Yong Xia, Jinyang Zheng
The trust region subproblem (TRS) is to minimize a possibly nonconvex quadratic function over a Euclidean ball. There are typically two cases for (TRS), the so-called ``easy case''…
On local minimizers of generalized trust-region subproblem
Jiulin Wang, Mengmeng Song, Yong Xia
Generalized trust-region subproblem (GT) is a nonconvex quadratic optimization with a single quadratic constraint. It reduces to the classical trust-region subproblem (T) if the co…
Polyak's convexity theorem, Yuan's lemma and S-lemma: extensions and applications
Mengmeng Song, Yong Xia
We extend Polyak's theorem on the convexity of joint numerical range from three to any number of quadratic forms on condition that they can be generated by three quadratic forms wi…
Trust-region and -regularized subproblems: local nonglobal minimum is the second smallest objective function value among all first-order stationary points
Jiulin Wang, Mengmeng Song, Yong Xia
The local nonglobal minimizer of trust-region subproblem, if it exists, is shown to have the second smallest objective function value among all KKT points. This new property is ext…